A386596 a(n) = Sum_{d|n} d * pi(n/d).

0, 1, 2, 4, 3, 10, 4, 12, 10, 15, 5, 31, 6, 21, 25, 30, 7, 45, 8, 48, 34, 29, 9, 83, 24, 34, 39, 65, 10, 102, 11, 71, 48, 42, 52, 134, 12, 47, 56, 128, 13, 141, 14, 94, 109, 55, 15, 199, 43, 108, 70, 109, 16, 169, 74, 174, 78, 65, 17, 300, 18, 71, 148, 160, 87, 204, 19, 137, 92, 216, 20, 351, 21, 82, 173, 153, 100, 238, 22, 308, 139, 89, 23, 409, 109, 94, 111

Offset: 1

Author

Wesley Ivan Hurt, Jul 26 2025

Keywords

• nonn
• look
• changed

Comments

Dirichlet convolution of n and pi(n).

Inverse Möbius transform of A333699(n).

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000720 (pi), A333699.

Programs

Maple

f:= proc(n) local d;
      add(d*numtheory:-pi(n/d),d=numtheory:-divisors(n))
end proc:
map(f, [$1..100]); # Robert Israel, Aug 26 2025

Mathematica

Table[Sum[d*PrimePi[n/d], {d, Divisors[n]}], {n, 100}]

Formula

a(n) = Sum_{d|n} A333699(d).